eqn not supported PGMFRACT(1) manual page Table of Contents

NAME

pgmfract - generate fractal as PGM picture

Synopsis

pgmfract [-s size] [-d depth] [-p xpos:ypos:distance]

Description

pgmfract computes a fractal and outputs it to standard output as PGM file. Each $x, y$ pixel of the picture corresponds to the complex number $c = x + y i$ in the formula $z' = z sup 2 + c$. The first iteration begins with $z = x + i y$, following iterations use the previously calculated value of $z'$. As soon as the absolute value of $z$ becomes larger than 2, it is known that the iteration will converge against infinity and the pixel is coloured depending on the number of iterations. Some values of $c$ never cause $z$ to become larger than 2, so the iteration depth has to be limited. If this limit is reached, the pixel will be black. The Mandelbrot set is the set of values for $c$, which never cause $z$ to converge against infinity, so limiting the depth causes a small error. Using a large enough depth minimizes this error.

Options

-s size
Change the picture size from the default of 600 pixel in each direction to size pixels.
-d depth
Change the maximum iteration depth from the default of 600 iterations to depth iterations.
-p xpos:ypos:distance
Change the interval of the complex start values from 0.0:0.0:2.0 to the new center xpos an ypos with an interval of distance in each direction.
-j cr:ci
Compute a julia set instead of a mandelbrot set by specifying a fixed value $c$ for iterations instead of a pixel dependent value $x + i y$. Interesting subsections from the mandelbrot set yield interesting julia sets.

Examples

Beautiful sections are:

pgmfract -p -0.5:0.0:1.5 >fractal.pgm

pgmfract -p -0.7660315:0.100861:0.0003 >fractal.pgm

pgmfract -p -1.252758:0.342541:0.007629 >fractal.pgm

pgmfract -p -0.368056:0.645833:0.097222 >fractal.pgm 

pgmfract -p -0.17596915:1.08649105:0.0000004 >fractal.pgm 

pgmfract -j -0.17596915:1.08649105 -p 0.0:0.0:0.01 >fractal.pgm 

pgmfract -d 2000 -p -0.74567846:0.09998153:0.00012307 >fractal.pgm 

pgmfract -d 2000 -j -0.74567846:0.09998153 -p 0.0:0.0:0.1 >fractal.pgm 

Author

Michael Haardt <michael@moria.de>.

History

The original version of this program has been written in 6502 Assembler for an Acorn Electron in 1985. From there, it went to Small-C for the Z80 on a PCW8256 in 1986 to ANSI-C and Linux in 1998.

See Also

pgm(5) eqn not supported


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